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Uncertainty from resolution and percentage uncertainty

Edexcel IAL Physics · WPH13 Practical Skills in Physics I

Uncertainty tells you how far from your reading the true value could be. Pearson's examiners use clear rules for finding it.

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Single readings

For a single reading, the uncertainty is half the resolution of the instrument:

Digital balance reading to 0.001 kg: uncertainty ±0.0005 kg.
Vernier calipers (0.1 mm): ±0.05 mm. Micrometer (0.01 mm): ±0.005 mm.
Digital voltmeter showing 2.36 V: ±0.005 V.

Do not confuse the resolution (the smallest interval) with the uncertainty (half of it here), and give a unit for each. A length found from two readings on a rule (one at each end) carries the uncertainty from both readings, so add them.

Percentage uncertainty

percentage uncertainty = (uncertainty / measured value) x 100%

Give it to 1 or 2 significant figures.
It lets you compare how good different measurements are and decide which one to improve.
For repeat readings, Pearson's guidance suggests that a percentage uncertainty below about 5% shows the measurement is probably repeatable.

Making it smaller

For a fixed uncertainty, a larger measurement gives a smaller percentage uncertainty. That is why we use long wires, large distances to a screen, many oscillations and stacks of thin objects. Choosing an instrument with a finer resolution helps too.

Worked example

A balance with resolution 0.001 kg gives a mass of 0.250 kg. Find the uncertainty and the percentage uncertainty.

Uncertainty = half the resolution = 0.0005 kg
Percentage uncertainty = 0.0005 / 0.250 x 100 = 0.2%

Answer: 0.250 kg ± 0.0005 kg, which is ± 0.2%

Key idea: Single reading: uncertainty = half the resolution. Percentage uncertainty = uncertainty / value x 100%, to 1 or 2 s.f. Bigger measurements give smaller percentage uncertainties.

Check yourself

A digital balance has a resolution of 0.01 g. What is the uncertainty in a single reading, in g?
Show answer
0.005 g. Half the resolution: 0.005 g.
A digital voltmeter reads 2.36 V. Find the percentage uncertainty, using half the resolution, to 2 s.f.
Show answer
0.21 %. Uncertainty = 0.005 V; 0.005 / 2.36 x 100 = 0.21%.
Vernier calipers (resolution 0.1 mm) give a length of 23.4 mm. Find the percentage uncertainty, to 2 s.f.
Show answer
0.21 %. 0.05 / 23.4 x 100 = 0.21%.
A thermometer reading to 1 °C shows 21 °C before and 45 °C after heating. Each reading is uncertain by half the resolution. Find the percentage uncertainty in the temperature rise, to 2 s.f.
Show answer
4.2 %. Rise = 24 °C; uncertainty = 0.5 + 0.5 = 1 °C (both readings count); 1 / 24 x 100 = 4.2%.
A length of 850 mm is found from two readings on a metre rule (resolution 1 mm), one at each end. Find the percentage uncertainty in the length, to 2 s.f.
Show answer
0.12 %. Uncertainty = 0.5 + 0.5 = 1 mm; 1 / 850 x 100 = 0.12%.
What is the resolution of an instrument?
- Half the smallest interval
- How close it reads to the true value
- The smallest measuring interval it can show
- How close repeated readings are
Show answer
The smallest measuring interval it can show. Resolution is the smallest interval; for a single reading the uncertainty is half of it.
Why does using a longer wire reduce the percentage uncertainty in its measured length?
- The same absolute uncertainty is a smaller fraction of a larger length
- Long wires have no zero error
- The metre rule becomes more precise
- A longer wire has a smaller resistance
Show answer
The same absolute uncertainty is a smaller fraction of a larger length. Percentage uncertainty = uncertainty / value; the value grows while the uncertainty stays the same.

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Last updated 8 November 2026. Spotted a mistake? Tell us.